It is cool, and I love your categories of discoveries. You are not alone. Here's a link you may want to read: http://www.research.att.com/~njas/sequences/?q=Goldbach&language=english&go=Search
--jim spike wrote: > Ja I did mean n = p*2^kp or n=(2^k)*p as Lloyd points out. I have > discovered a cool property of those numbers, altho surely not an original > discovery. All my mathematical discoveries fall into two sets: those > notions that have been known since before the Permian extinction, and those > notions that are original with me but are wrong. > > I was looking at Goldbach's conjecture, that any even number above 2 can be > expressed as the sum of two primes. So I wondered how many different ways > can a number be expressed as the sum of two primes? Let P(n) be the number > of ways, assuming the number 1 as not prime, but twice a prime counts in > P(n). So for instance P(14)=2 because of 3+11 and 7+7 but not 13+1. So > Goldbach conjectures that P(n)>0 for all even integers more than 2. > > There may be a standard terminology for this concept, I just don't know what > it is. > > I calculated P(n) for all evens up to 800,000 and found that in general P(n) > increases as a constant times n^.75 but if one graphs P(n) against n, one > sees a cool almost fractal pattern. The numbers separate into apparent > layers. The lowest layer, corresponding to about .12*n^.75 contains most of > the numbers, but a second layer forms above that one. I found that that > second layer is made up of factors of 6. another layer above that contains > numbers that are a factor of 30. Not surprisingly, a fourth layer contains > factors of 210. I guessed that still another layer would contain factors of > 2310 (check) and that P(30030) should be still another layer. Altho I have > only one example, the P(factors of 510510) soar still higher. > > I know this is correct, therefore it must be ancient knowledge. Is this > cool or what? > > spike > > > >> -----Original Message----- >> From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On >> Behalf Of Lloyd Miller >> Sent: Friday, October 20, 2006 12:26 PM >> To: The Great Internet Mersenne Prime Search list >> Subject: Re: [Prime] name please for n = 2^kp >> >> >> erm I think he means n=(2^k)*p > > > > > _______________________________________________ > Prime mailing list > [email protected] > http://hogranch.com/mailman/listinfo/prime _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
